اثرات سیاست پولی کوتاه مدت و بلند مدت در یک مدل تعادل عمومی با ذخایر بانک

This paper presents a dynamic general equilibrium model that allows the distinct short-run and long-run effects of monetary policy to be explained. There are two main features of the model. The first is the consideration of a financial intermediary that must use money to meet legal reserve requirements. The second is the monetary policy mechanism: The increase in the quantity of money goes first to the financial intermediaries, which can lend the new amount of money to firms since the legal reserve requirements have been fulfilled and there are no new deposits. The increasing investment of firms is accompanied by higher production and consumption, which constitute the short-run effects of monetary policy. As time passes, the additional quantity of money reaches the consumers, which then increases their deposits. The reserves therefore rise, the real short-run effects disappear, and the price level becomes higher as a result of the greater amount of money.

Over the last 50 years, the economic literature has produced a large amount of work exploring the role that money plays in an economy. This fact is in part a consequence of the unsatisfactory state of the modern monetary theory, which involves some problems that have been pointed out by, among others, Samuelson (1968), Hahn (1993), Lucas (1993) and Wallace, 1997 and Wallace, 1998. One of the more fundamental problems is the failure of the general equilibrium theory to incorporate money into its standard models in a sound way, able to explain the disparate long-run and short-run effects of changes in the quantity of money. As noted by Lucas (1996) and Wallace (1997), a great part of the research effort made in macroeconomics since the 1920s has been an attempt to explain these distinct effects. As is well known, the long-run effects of changes in the quantity of money are mainly nominal, while the short-run effects are predominantly real. In particular and as has been documented among many others by McCandless and Weber (1995),1Leeper et al. (1997), King and Watson (1997) and Monadjemi and Huh (1998), there is empirical evidence showing that, in the long-run, there is a high positive correlation between the growth rate of the money supply and inflation, and that, on the contrary, there is no long-run correlation between the growth rates of money and real output. However, when the short-run is analyzed, the quantity of money appears as an important variable positively correlated with output. Together with these dichotomy between nominal and real effects, changes in the quantity of money also imply two seemingly contradictory facts in the interest rates, likewise linked to the long- and short-run. On the one hand, in the long-run, there is empirical evidence that supports a positive relation between money and interest rates, in the line of that present in the Fisher equation. On the other hand, in the short-run, the empirical evidence shows that money and interest rates are negatively related, which is consistent with the interaction of money supply and demand and the so-called liquidity effect. This empirical evidence on the relationship between money and interest rates has been recently commented on and reviewed by Bernanke and Mihov (1998), Christiano, Eichenbaum and Evans (1999) and Monnet and Weber (2001). 2 As commented above, the observation of all these disparate long-run and short-run effects of changes in the quantity of money is, even today, challenging. Contributing to this research issue, this paper presents a dynamic general equilibrium model that can explain both the long-run and the short-run effects of monetary policy. There are two main features of the proposed model. The first is the consideration of a financial intermediary, that plays a role in facilitating production and capital accumulation, and that must use money to meet legal reserve requirements. The second feature is simplicity. The model is a representative agent model with no aggregate uncertainty and complete markets, where the production and financial sectors are integrated. Indeed, the resulting model is almost identical to a basic optimal growth model where the use of money is motivated by a cash-in-advance constraint. These two characteristics allow the real and nominal effects of distinct monetary policies to be studied from a simple, clear and intuitive perspective. The closest reference for this paper is that by Chari, Jones, and Manuelli (1995). These authors also study the real effects of monetary policy in a general equilibrium model with banks required to hold reserves. However, they focus exclusively in the long-run, make use of more sophisticated models, and explain the real effects of the monetary policy in a different way. In particular, Chari, Jones, and Manuelli (1995) consider a model with two types of capital, one of them intermediated through the banking system. The existence of a reserve requirement ratio creates a wedge between the marginal products of the two types of capital in the economy, which, in turn, distorts the capital mix. Therefore, in the Chari, Jones and Manuelli model, changes in the reserve requirements have real effects because these modifications alter the wedge between the capital marginal products and thus the capital mix. As commented above, this paper proposes an alternative point of view to explain the real effects of the monetary policy. The basic idea can be found in Hume (1752), and has been considered by Wallace (1997) in a schematic absence-of-double-coincidence model of money able to justify the existence of money as well as the disparate long-run and short-run effects of changes in the quantity of money. Hume (1752) expresses this idea as follows: In my opinion, it is only in this interval or intermediate situation, between the acquisition of money and rise of prices, that the increasing quantity of gold and silver is favourable to industry. When any quantity of money is imported into a nation, it is not at first dispersed into many hands, but is confined to the coffers of a few persons, who immediately seek to employ it to advantage. In particular, as happens in the real economy, in the model presented here, the increase in the quantity of money goes first to the financial intermediaries. The bank safeboxes, are, in Hume's words, the coffers of a few persons. The financial intermediaries use this new quantity of money to finance the purchase of additional capital production factor. Since the legal reserve requirements have already been fulfilled (there have not been new deposits), the new money can be used to make new loans to firms, which increase their investment, and, therefore, the present and future output. These are the short-run effects explained by this model, both on output as well as on interest rates, since the marginal productivity of capital is also modified. As time passes, the additional quantity of money reaches the consumers through the payment of the production input services. Households increase their deposits, banks calculate their reserve over the new amount of deposits, and the real short-run effects disappear since they are based on the existence of available money in excess of the legal requirements. Finally, in the long-run, the additional money in the economy results in a higher demand of final goods and services and in higher prices, given that the real effects have vanished. These are the guidelines of the model described, explained and solved in Section 2 of this paper. In Section 3 the effects of alternative monetary policies are discussed and studied, both in the short- and long-run. Finally, Section 4 concludes the paper and proposes future research on this line.

Empirical researchers have found that monetary policy has disparate long-run and short-run effects. As is widely documented, the short-run effects are predominantly real, while the long-run effects of changes in the quantity of money are mainly nominal. However, modern monetary theory has not been able to satisfactorily explain this dichotomy. In this paper I contribute to the existing literature proposing a cash-in-advance in everything model that allows the distinct short- and long-run effects of monetary policy to be explained. As suggested by Chari, Jones and Manuelli (1995), this analysis shifts its focus from printing money toward the banking and financial regulation. In this respect, there are two main features of the presented dynamic general equilibrium model. The first is the consideration of a financial intermediary, that facilitates production and capital accumulation, and that must use money to meet legal reserve requirements. The second is the monetary policy mechanism, in which the financial intermediary plays a basic role. As happens in modern economies, in the model I present the increase in the quantity of money goes first to the financial intermediaries. These financial intermediaries use the new amount of money to finance the purchase of additional capital production factor: since the legal reserve requirements have been fulfilled and there are no new deposits, the new money can be used to make new loans to firms. The increasing investment of firms is accompanied by higher production and consumption, which constitute the short-run effects of monetary policy together with the decrease in the interest rates, the consequence of a lower marginal productivity of capital. With time, the additional quantity of money reaches the consumers through the payment of production input services. Households increase their deposits, banks calculate their reserve over the new amount of deposits, and the real short-run effects disappear since they are based on the existence of available money in excess of the legal requirements. Finally, in the long-run, the additional money in the economy results in a higher demand of final goods and services and in higher prices given that the real effects have vanished. The existence of a financial intermediary that immediately employs the new amount of money to increase investment is therefore the key stone of the model. When the monetary policy is implemented through permanent changes in the legal reserve coefficient, different short-run and long-run appears. As in the previous case, the lower legal reserve requirements come together with new loans to firms, increasing investment and higher production and consumption, but nominal effects are distinct: since money supply does not increase, there are not inflationary processes, and nominal interest rates decrease. Short-run dynamics are also quite distinct, in particular for prices and interest rates. One additional characteristic of the presented model is its simplicity. Taking a disaggregate dynamic general equilibrium as the starting point, money is introduced in the sense proposed by Clower (1967). Once the monetary general equilibrium of this cash-in-advance economy has been defined, an equivalent real general equilibrium is obtained, and, from this, an equivalent social planner's problem is formulated. This social planner's problem allows the monetary policy effects to be easily analyzed, since, as explained, the increase in the money supply is equivalent, from the production perspective, to a temporary decrease in the legal reserve coefficient. This model is able to explain the main empirical facts concerning monetary policy. In particular, when money supply increases, it is obtained a short-run positive correlation between the quantity of money and output that vanishes in the long-run, a log-run positive relationship between inflation and growth of money supply, and a nominal interest rate decrease in the short-run that reverses in the long-run. The long-run relationship between growth and reserve requirements suggested by Chari, Jones and Manuelli is also found, together with new possibilities to explain the short-run effects. The quantitative magnitude of all these effects depends on two aspects. First, on the proximity of the economy to its steady state, and, secondly, on the specific parameter values. Future research lines on this model pass therefore through calibration analyses as well as through simulation exercises. Theoretical extensions are of course very interesting, in particular those incorporating uncertainty and a wider variety of assets.